Abstract

The method of smoothing is used to study sound propagation and scattering in a realistic shallow‐water environment with a randomly rough water–sediment interface. A mean fieldwave equation for the coherent acoustic field is obtained that has a complex‐valued attenuation coefficient that is localized at the mean interface. The solution of the mean field equation, under highly idealized conditions, is derived and discussed. The branch point and pole singularities are found to be related to the head wave mode and the Biot–Tolstoy rough boundary wave mode, respectively. Also obtained is the coherent plane‐wave reflection coefficient which is found to vanish when the acoustic frequency and the incident angle of the plane wave satisfy a certain resonant condition. For testing the mean field equation, a stochastic full‐wave forward propagation PE model is developed for Monte Carlo simulations. The numerical results show that the coherent field obtained by an ensemble average over many realizations is in agreement with that obtained by solving the mean field equation just once. The Monte Carlo simulations also yield additional useful information about higher‐order moments of the acoustic field. [Work supported by ONR.]